Howdy shelbysoto,
If your goal is simply to have a search box, well you could have a standard HTML search form that submit to the tri.be events page. If you want to have the View As drop down, date selector, and so forth, then it will get a lot more complicated. There are a lot of JS scripts powering those, and they all expect to be included on the events page. You would have to rewrite a lot of code in new JS files for inclusion on other pages, sadly. Probably not worth it.
Did that answer your question? Please let me know if I can elaborate on anything. Thanks!
– Brook